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\title{Turbulent Inflow Tool}
\author{Jay and Peter}
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\begin{document}
\maketitle

\section{Abstract}

This tool helps you to create all necessary input to utilize the turbulent inflow boundary condition in OpenFOAM.

\section{Theory}

Wait for Jay's write-up.

\subsection{Uniform model}

\begin{equation}
   u = \bar\phi
   \label{Eq1}
\end{equation}

\begin{equation}
   \vectr{u} = u\,\vectr{N}
   \label{Eq2}
\end{equation}

\subsection{Exponential model}

\begin{equation}
   \phi = \bar\phi \left( \frac{\vectr{n} \cdot \vectr{x} }{d_0} \right)^\alpha
   \label{Eq11}
\end{equation}

\begin{equation}
   \ell_{u,y} = R_{uy:ux} \, \ell_{u,x}   \qquad   \ell_{u,z} = R_{uz:ux} \, \ell_{u,x}
   \label{Eq12}
\end{equation}
\begin{equation}
   \ell_{v,y} = R_{vy:vx} \, \ell_{v,x}   \qquad   \ell_{v,z} = R_{vz:vx} \, \ell_{v,x}
   \label{Eq13}
\end{equation}
\begin{equation}
   \ell_{w,y} = R_{wy:wx} \, \ell_{w,x}   \qquad   \ell_{w,z} = R_{wz:wx} \, \ell_{w,x}
   \label{Eq14}
\end{equation}



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